Multivariate image regression (MIR): implementation of image PLSR?first forays

In the effort of analysing multivariate images, image PLS has been considered interesting. In this paper, image PLS (MIR) is compared with image PCA (MIA) by studying a comparison data set. While MIA has been commercially available for some time, image PLS has not. The kernel PLS algorithm of Lindgren has been implemented in a development environment which is a combination of G (LabVIEW) and MATLAB. In this presentation the power of this environment, as well as an early example in image regression, will be demonstrated. With kernel PLS, all PLS vectors (eigenvectors and eigenvalues) can be calculated from the joint variance–covariance (X′Y and Y′X) and association (Y′Y and X′X) matrices. The dimensions of the kernel matrices X′YY′X and Y′XX′Y are K × K (K is the number of X-variables) and M × M (M is the number of Y-variables) respectively. Hence their size is dependent only on the number of X and Y-variables and not on the number of observations (pixels), which is crucial in image analysis. The choice of LabVIEW as development platform has been based on our experience of a very short implementation time combined with user-friendly interface possibilities. Integrating LabVIEW with MATLAB has speeded up the decomposition calculations, which otherwise are slow. Also, algorithms for matrix calculations are easier to formulate in MATLAB than in LabVIEW. Applying this algorithm on a representative test image which shows many of the typical features found in technical imagery, we have shown that image PLS (MIR) decomposes the data differently than image PCA (MIA), in accordance with chemometric experience from ordinary two-way matrices. In the present example the Y-reference texture-related image used turned out to be able to force a rather significant ‘tilting’ compared with an ‘ordinary MIA’ of the primary structures in the original, spectral R/G image.